Nearly round spheres look convex

Ludovic Rifford

Description

Nearly round spheres look convex Ludovic Rifford Universite de Nice - Sophia Antipolis (Joint work with A. Figalli and C. Villani) Ludovic Rifford Workshop on Optimal transportation and applications

• nearly round spheres


• ?? expx


• expx


• round sphere


• injectivity domains


• geodesic between


• compact riemannian


• universite de nice


• look convex


• txm ??

Sujets

• Antipolis
• Universidad de Niza Sophia Antipolis

Informations

• Publié par: pefav
• Nombre de lectures: 11
• Langue: English

Extrait

Nearly

(Joint

round

spheres

Ludovic

look

Rifford

Universit´edeNice-SophiaAntipolis

work

with

A.

Ludovic Rifford

Figalli

and

C.

convex

Villani)

Workshop on Optimal transportation and applications

The statement

Theorem (Figalli, R, Villani ’09) Let(M,g)be a C 4 perturbation of the round sphereS n . Then all injectivity domains of M are uniformly convex.

Ludovic Rifford

Workshop on Optimal transportation and applications

Injectivity domains

Let (M,g) be a smooth compact Riemannian manifold and x∈M call exponential mapping from Webe fixed.x, the mapping defined as

exp x

:T x M v

−→ 7−→

M exp x (v) :=γ v (1),

whereγ v : [0,1]→Mis the unique geodesic starting atxwith speed ˙γ v (0) =v.

Ludovic Rifford

Workshop on Optimal transportation and applications